On the Adequacy of Global Pressure Gain as the Performance Metric for Rotating Detonation Combustors

Abstract

Detonation-based combustors are attractive for potential increases in thermodynamic efficiency, leading to improved thrust or work production. Fundamentally, a detonation produces less entropy at the flame front. Rotating detonation combustors (RDCs) are designed to provide this gain in a compact form. However, experimentally evaluating this is challenging due to the unsteady, non-uniform, and complex flow within RDCs along with being incapable of measuring entropy. Thus, in the RDC literature, the thermodynamic gain is equated to an increase in total pressure globally across the RDC, termed “pressure gain” (PG). The RDC community widely accepts PG as a preferred performance metric. This work comprehensively evaluates experimental measurements of this global PG metric.

One must average the non-uniform exit flow to define a singular exit total pressure for an RDC. Experimentally, this is done through the Equivalent Available Pressure (EAP) methodology. This work demonstrates that the EAP is equivalent to area-averaging and does not conserve the exiting flow's momentum, energy, or entropy. Additionally, the concept of PG is not unique, as shown by applying various averaging methods to high-fidelity, three-dimensional RDC simulations. For instance, the average total pressure varies by 10-20% depending on the assumed outlet state and whether one uses the RDC for work or thrust production. Perhaps even more importantly, the EAP significantly underpredicts, by 2.5-38%, the other average total pressures. Therefore, the experimental PG has limitations from a theoretical perspective.

Nevertheless, the EAP method of experimentally measuring PG is adapted and applied to an axial-air inlet RDC with a nozzle, A8/A3.1=2.31. A parametric study of air mass fluxes, from 193 kg/m2/s to 773 kg/m2/s, and equivalence ratios, from 0.6 to 1.2, of hydrogen/air chemistry was investigated. No positive PG was measured, with the best performance being a total pressure loss of 20%. A detailed uncertainty analysis reveals that the experimental PG method is prone to significant experimental uncertainties, such as resolving the base drag acting upon the bluff nozzle. When combined, the uncertainties in the PG result are ±6%, a 30% relative change of the measured -20%. Such precision limitations pose practical challenges for future demonstrations of a definitive positive PG. Additionally, further improvements to the accuracy and precision of EAP and PG come from evaluating the area-averaged exit Mach number using a static pressure measurement.

This work also varied the combustor length from 79 mm to 137 mm, to induce significant changes to the properties of the detonation wave(s). The PG only changed by at most 5% despite the wave speed changing by 38%. Furthermore, the changes in PG are less than the uncertainty; thus, the PG is invariant to such changes. Conversely, a change to the injection geometry investigated in this work exhibited a measurable decrease in PG (greater than 6%), which is attributed to an augmentation of the backflow in the system from intentionally worsening the injector diodicity. Overall, there are many competing physics within a RDC (e.g., wave strength, backflow, secondary combustion, secondary waves, etc.), and the global PG has different sensitivities to the individual processes, limiting the metric's usefulness. Ultimately, while PG can readily assess the impact of inlet performance on the overall performance of RDC, the concerns about not conserving any thermodynamic quantity, high experimental uncertainty, and insensitivity to several key features of the RDC flowfield limits PG as an all-inclusive performance metric.